In this study, we consider the indirect loop effects induced by a 3-form field on the muon electromagnetic dipole moment defined by \(a_\mu = (g-2)_\mu /2\) , which might solve the long-standing muon \(g-2\)  anomaly [1]}. Currently, the comparison between the Standard Model (SM) prediction and the experimental data shows a remarkable \(\sim 4.25\sigma \)  discrepancy [2]}:
\(\Delta a_\mu = a_\mu ^{\rm Exp} - a_\mu ^{\rm SM} = (251\pm 59)\times 10^{-11},\) 
